With all the fad diets advertised on TV, a researcher wanted to know if there wa

Question

With all the fad diets advertised on TV, a researcher wanted to know if there was a significant difference in weight loss depending on which new fad diet you were on. Over the course of 2 weeks, a total of 12 male volunteers who weighed the same and had similar lifestyles were broken up into 3 groups: Diet 1 Diet 2, and Diet 3. Conduct an ANOVA on the following table with alpha-0.5 to determine if at least one of the diets has significantly different weight loss compared to the other two. Diet 1 Diet 2 13 12 Diet 3 1. What are the null and alternative hypotheses? mean weight loss from Diet 2 Ho: Mean weight loss from Diet 1 from Diet 3 Ha: Mean weight loss from Diet 1 > mean weight loss from Diet 2 > mean weight loss from Diet 3 a. mean weight loss b. H Mean weight loss from Diet 1- mean weight loss from Diet 2- mean weight loss from Diet 3 Ha: At least one mean weight loss is significantly different c. H: At least one mean weight loss is significantly different H: Mean weight loss from Diet 1> mean weight loss from Diet 2 > mean weight loss from Diet 3 d. Ho Mean weight loss from Diet 1- mean weight loss from Diet 2-mean weight loss from Diet 3 HA: Mean weight loss from Diet 1

Explanation / Answer

QUESTION 1

Here /option b is correct here about hypothesis problem

Question 2.

df(between) = 2

Question 3

df(within) = (4-1) *3 = 9

Question 4

Critival value for dF1  = 2, dF2 = 9

F(critical) = F(0.05, 2, 9) = 4.2565

Question 5

The completed ANOVA table is

SS(between) = 96.5

Question 6

MS (between) = 48.25

Question 7

MS (within) = 9.5

QUestion 8

F = 48.25/9.5 = 5.0789

QUestion 9

Here we reject the null hypotheis becuase test statistic fall in the rejection region Option D is correct here.  

ANOVA Source of Variation SS df MS F P-value F crit Between Groups 96.5 2 48.25 5.078947 0.033383 4.256495 Within Groups 85.5 9 9.5 Total 182 11

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